an operation * on the set of R of real numbers is defined by
a*b= 2a +2b-3 for all a,b£R. Find the inverse x£R
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2?
what is the identity element? I'm assuming it's 0, since only addition is involved. So, you want to find c such that x*c = 0
x*c = 2x+2c-3 = 0
c = 3/2 - x
To find the inverse of an element, let's solve for x in the equation:
a * x = 2a + 2x - 3
Given that the operation "*" is defined as:
a * b = 2a + 2b - 3,
we can substitute b with x in the definition:
a * x = 2a + 2x - 3.
Now, let's isolate x on one side of the equation:
2x - 3 = a * x - 2a,
2x - a * x = -2a + 3,
x(2 - a) = -2a + 3,
x = (-2a + 3)/(2 - a).
Therefore, the inverse x in the set of real numbers R is given by the equation:
x = (-2a + 3)/(2 - a).